UV Unwrap - Object - Select Faces ONLY - and Paint UV
1) You started with a resetted UV mesh (all faces overlapping and occupying all UV space available), then you re-unwrapped part of the mesh. The two unwrapping operation got some overlapping, you can see it if you select all faces. The correct way is to unwrap one time only, then select the faces you want to paint, turn the 3D window into "texture paint" mode, enable the button named "face selection masking for painting" and paint in the 3D window. 

2) The stroke/fill controls you tried to use are referred to the grease pencil only. In the UV/image window, you can acces to the paint controls pressing T, to show all tools tabs on the left of the window.